GEOMETRICAL EXPONENTS IN THE INTEGER QUANTUM HALL-EFFECT

We point out that the extended Chalker-Coddington model in the ''class ical'' limit, i.e. the limit of large disorder, shows crossover to the so-called ''smart kinetic walks''. The reason why this limit has prev iously been identified with ordinary percolation is, presumably, that the localization length exponents nu coincide for the two problems. Ot her exponents, like the fractal dimension D, differ. This gives an opp ortunity to test the consistency of the semiclassical picture of the l ocalization-delocalization transitions in the integer quantum Hall eff ect. We calculate numerically, using the extended Chalker-Coddington m odel, two exponents tau and D that characterize critical properties of the geometry of the wave function at these transitions. We find that the exponents, within our precision, are equal to those of two-dimensi onal percolation, as predicted by the semiclassical picture.